Dustin Pedroia contributed a two-run homer in Boston's sixth win in seven games.
Daisuke Matsuzaka (4-0) gave up five hits and three runs in five-plus innings to get the win.
Texas had won its previous two games.
Luis Mendoza (0-2) retired the first eight men he faced, but then wilted under the Boston attack. He allowed five hits and seven runs in three-plus innings.
With two away and the bases empty in the third, Jed Lowrie doubled off Mendoza. Jacoby Ellsbury and Pedroia drew walks to load the bases and Ortiz then unloaded on Mendoza's first offering, driving it over the wall in left-center.
Ortiz entered the game with just seven hits in 63 at-bats.
Boston added five runs in the fourth, two of them on Pedroia's homer.